/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2003 Ferdinando Ametrano

 Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb

 Copyright (C) 2004, 2005 StatPro Italia srl

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <https://www.quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT

 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS

 FOR A PARTICULAR PURPOSE.  See the license for more details.

*/

/*! \file ornsteinuhlenbeckprocess.hpp

    \brief Ornstein-Uhlenbeck process

*/

#ifndef quantlib_ornstein_uhlenbeck_process_hpp

#define quantlib_ornstein_uhlenbeck_process_hpp

#include <ql/stochasticprocess.hpp>

namespace QuantLib {

    //! Ornstein-Uhlenbeck process class

    /*! This class describes the Ornstein-Uhlenbeck process governed by

        \f[

            dx = a (r - x_t) dt + \sigma dW_t.

        \f]

        \ingroup processes

    */

    class OrnsteinUhlenbeckProcess : public StochasticProcess1D {

      public:

        OrnsteinUhlenbeckProcess(Real speed,

                                 Volatility vol,

                                 Real x0 = 0.0,

                                 Real level = 0.0);

        //! \name StochasticProcess interface

        //@{

        Real drift(Time t, Real x) const override;

        Real diffusion(Time t, Real x) const override;

        Real expectation(Time t0, Real x0, Time dt) const override;

        Real stdDeviation(Time t0, Real x0, Time dt) const override;

        //@}

        Real x0() const override;

        Real speed() const;

        Real volatility() const;

        Real level() const;

        Real variance(Time t0, Real x0, Time dt) const override;

      private:

        Real x0_, speed_, level_;

        Volatility volatility_;

    };

    // inline

    inline Real OrnsteinUhlenbeckProcess::x0() const {

        return x0_;

    }

    inline Real OrnsteinUhlenbeckProcess::speed() const {

        return speed_;

    }

    inline Real OrnsteinUhlenbeckProcess::volatility() const {

        return volatility_;

    }

    inline Real OrnsteinUhlenbeckProcess::level() const {

        return level_;

    }

    inline Real OrnsteinUhlenbeckProcess::drift(Time, Real x) const {

        return speed_ * (level_ - x);

    }

    inline Real OrnsteinUhlenbeckProcess::diffusion(Time, Real) const {

        return volatility_;

    }

    inline Real OrnsteinUhlenbeckProcess::expectation(Time, Real x0,

                                               Time dt) const {

        return level_ + (x0 - level_) * std::exp(-speed_*dt);

    }

    inline Real OrnsteinUhlenbeckProcess::stdDeviation(Time t, Real x0,

                                                Time dt) const {

        return std::sqrt(variance(t,x0,dt));

    }

}

#endif